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The stochastic dynamic damage locating vector approach is a vibration-based damage localization method based on a finite element model of a structure and output-only measurements in both reference and damaged states. A stress field is computed for loads in the null space of a surrogate of the change in the transfer matrix at the sensor positions for some values in the Laplace domain. Then, the damage location is related to positions where the stress is close to zero. Robustness of the localization information can be achieved by aggregating results at different values in the Laplace domain. So far, this approach, and in particular the aggregation, is deterministic and does not take the uncertainty in the stress estimates into account. In this paper, the damage localization method is extended with a statistical framework. The uncertainty in the output-only measurements is propagated to the stress estimates at different values of the Laplace variable, and these estimates are aggregated based on statistical principles. The performance of the new statistical approach is demonstrated both in a numerical application and a lab experiment, showing a significant improvement of the robustness of the method due to the statistical evaluation of the localization information.

A theorem on damage localization from flexibility changes has been proven recently,
where it has been shown that the image of the change in flexibility δF between
damaged and reference states of a structure is a basis for the influence lines of stress
resultants at the damaged locations. This damage localization approach can operate on
output-only vibration measurements from damaged and reference states, and a finite
element model of the structure in reference state is required. While the localization
approach is based on purely mechanical principles, an estimate of the image of δF is
required from the data that is subject to statistical uncertainty due to unknown noise
excitation and finite data length. In this paper, this uncertainty is quantified from the
measurements and a statistical framework is added for the decision about damaged
elements. The combined approach is successfully applied to a numerical simulation
and to a cantilever beam in a lab experiment.

The subject of damage localization is an important issue for Structural Health Monitoring (SHM) particularly in mechanical or civil structures under ambient excitation. In this paper, the statistical subspacebased damage localization method has been applied on a benchmark application, namely a 1/200 scale model of the Saint-Nazaire Bridge, which is a cable-stayed bridge located on the Loire River near the river’s mouth. The employed damage localization method combines data-driven features with physical parameter information from a finite element model in statistical tests, avoiding typical ill-conditioning problems of FE model updating. Damage is introduced in the mockup for cable failures on some of the 72 cables. The purpose of the experiment is to assess the capability of damage assessment methods to find a cable failure.

The Stochastic Dynamic Damage Locating Vector (SDDLV) approach is a vibration-based damage localization method based on both a finite element model of a structure and modal parameters estimated
from output-only measurements in the damage and reference states. A statistical version of the Approach takes into account the inherent uncertainty due to noisy measurement data. In this paper, the effect of temperature fluctuations on the performance of the method is analyzed in a model-based approach using a finite element model with temperature dependent parameters. Robust damage localization is carried out by rejecting the temperature influence on the identified modal parameters in the damaged state. The algorithm is illustrated on a simulated structure.

In Operational Modal Analysis, the modal parameters (natural frequencies, damping ratios and mode shapes) obtained from Stochastic Subspace Identification (SSI) of a structure, are afflicted with statistical uncertainty. For evaluating the quality of the obtained results it is essential to know the respective confidence intervals of these figures. In this paper we present algorithms that automatically compute the confidence intervals of modal parameters obtained from covarianceand data-driven SSI of a structure based on vibration measurements. They are applied to the monitoring of the modal parameters of a prestressed concrete highway bridge during a progressive damage test that was accomplished within the European research project IRIS. Results of the covariance- and data-driven SSI are compared.

Structural health monitoring with statistical methods during progressive damage test of S101 Bridge
(2014)

For the last decades vibration based damage detection of engineering structures has become an important issue for maintenance operations on transport infrastructure. Research in vibration based structural damage detection has been rapidly expanding from classic modal parameter estimation to modern operational monitoring. Since structures are subject to unknown ambient excitation in operation conditions, all estimates from the finite data measurements are of statistical nature. The intrinsic uncertainty due to finite data length, colored noise, non-stationary excitations, model order reduction or other operational influences needs to be considered for robust and automated structural health monitoring methods. In this paper, two subspace-based methods are considered that take these statistical uncertainties into account, first modal parameter and their confidence interval estimation for a direct comparison of the structural states, and second a statistical null space based damage detection test that completely avoids the identification step. The performance of both methods is evaluated on a large scale progressive damage test of a prestressed concrete road bridge, the S101 Bridge in Austria. In an on-site test, ambient vibration data of the S101 Bridge was recorded while different damage scenarios were introduced on the bridge as a benchmark for damage identification. It is shown that the proposed damage detection methodology is able to clearly indicate the presence of structural damage, if the damage leads to a change of the structural system.

This paper deals with uncertainty considerations in damage diagnosis using the stochastic subspace-based damage detection technique. With this method, a model is estimated from data in a (healthy) reference state and confronted to measurement data from the possibly damaged state in a hypothesis test. Previously, only the uncertainty related to the measurement data was considered in this test, whereas the uncertainty in the estimation of the reference model has not been considered. We derive a new test framework, which takes into account both the uncertainties in the estimation of the reference model as well as the uncertainties related to the measurement data. Perturbation theory is applied to obtain the relevant covariances. In a numerical study the effect of the new computation is shown, when the reference model is estimated with different accuracies, and the performance of the hypothesis tests is evaluated for small damages. Using the derived covariance scheme increases the probability of detection when the reference model estimate is subject to high uncertainty, leading to a more reliable test.

This paper deals with vibration-based damage localization and quantification from output-only measurements. We describe an approach which operates on a data-driven residual vector that is statistically evaluated using information from a finite element model, without updating the parameters of the model. First, the damaged elements are detected in statistical tests, and second, the damage is quantified only for the damaged elements. We propose a new residual vector in this context that is based on the transfer matrix difference between reference and damaged states, and compare it with a previously introduced subspace-based residual. We show localization and quantification on both residuals in simulations.

In the last ten years, monitoring the integrity of the civil infrastructure has been an active research topic, including in connected areas as automatic control. It is common practice to perform damage detection by detecting changes in the modal parameters between a reference state and the current (possibly damaged) state from measured vibration data. Subspace methods enjoy some popularity in structural engineering, where large model orders have to be considered. In the context of detecting changes in the structural properties and the modal parameters linked to them, a subspace-based fault detection residual has been recently proposed and applied successfully, where the estimation of the modal parameters in the possibly damaged state is avoided. However, most works assume that the unmeasured ambient excitation properties during measurements of the structure in the reference and possibly damaged condition stay constant, which is hardly satisfied by any application. This paper addresses the problem of robustness of such fault detection methods. It is explained why current algorithms from literature fail when the excitation covariance changes and how they can be modified. Then, an efficient and fast subspace-based damage detection test is derived that is robust to changes in the excitation covariance but also to numerical instabilities that can arise easily in the computations. Three numerical applications show the efficiency of the new approach to better detect and separate different levels of damage even using a relatively low sample length.

Temperature variation can be a nuisance that perturbs vibration based structural health monitoring (SHM) approaches for civil engineering structures. In this paper, temperature affected vibration data is evaluated within a stochastic damage detection framework, which relies on a null space based residual. Besides two existing temperature rejection approaches – building a reference state from an averaging method or a piecewise method – a new approach is proposed, using model interpolation. In this approach, a general reference model is obtained from data in the reference state at several known reference temperatures. Then, for a particular tested temperature, a local reference model is derived from the general reference model. Thus, a well fitting reference null space for the formulation of a residual is available when new data is tested for damage detection at an arbitrary temperature. Particular attention is paid to the computation of the residual covariance, taking into account the uncertainty related to the null space matrix estimate. This improves the test performance, contrary to prior methods, for local and global damages, resulting in a higher probability of detection (PoD) for the new interpolation approach compared to previous approaches.

The local asymptotic approach is promising for vibration-based fault diagnosis when associated to a subspace-based residual function and efficient hypothesis testing tools. It has the ability of detecting small changes in some chosen system parameters. In the residual function, the left null space of the observability matrix associated to a reference model is confronted to the Hankel matrix of output covariances estimated from test data. When this left null space is not perfectly known from a model, it should be replaced by an estimate from data to avoid model errors in the residual computation. In this paper, the asymptotic distribution of the resulting data-driven residual is analyzed and its covariance is estimated, which includes also the covariance related to the reference null space estimate. The importance of including the covariance of the reference null space estimate is shown in a numerical study.

The local asymptotic approach is promising for vibration-based fault diagnosis when associated to a subspace-based residual function and efficient hypothesis testing tools. It has the ability of detecting small changes in some chosen system parameters. In the residual function,the left null space of the observability matrix associated to a reference model is confronted to the Hankel matrix of output covariances estimated from test data. When this left null space is not perfectly known from a model, it should be replaced by an estimate from data to avoid model errors in the residual computation. In this paper, the asymptotic distribution of the resulting data-driven residual is analyzed and its covariance is estimated, which includes also the covariance related to the reference null space estimate. The advantages of the data-driven residual are demonstrated in a numerical study, and the importance of including the covariance of the reference null space estimate is shown, which increases the detection Performance.

For the last decades vibration based identification of damage on civil Engineering structures has become an important issue for maintenance operations on transport infrastructure.
Research in that field has been rapidly expanding from classic modal Parameter estimation using measured excitation to modern operational monitoring. Here the difficulty is to regard to the specific environmental and operational influence to the structure under observation. In this paper, two methods accounting for statistical and/or operational uncertainties are applied to measurement data of a progressive damage test on a prestressed concrete bridge. On the base of covariance driven Stochastic Subspace Identification (SSI) an algorithm is developed to monitor and automatically compute confidence intervals of the obtained modal parameters. Furthermore, a null space based non-parametric damage detection method, utilizing a statistical χ2 type test is applied to the measurement data. It can be shown that for concrete bridges the proposed methodology is able to clearly indicate the presence of structural damage, if the damage leads to a change of the structural system.

For the last decades vibration based damage detection of engineering structures has become an important issue for maintenance operations on transport infrastructure. Research in vibration based structural damage detection has been rapidly expanding from classic modal parameter estimation to modern operational monitoring. Methodologies from control Engineering especially of aerospace applications have been adopted and converted for the application on civil structures. Here the difficulty is to regard to the specific environmental and operational influence to the structure under observation. A null space based damage detection algorithm is tested for its sensitivity to structural damage of a prestressed concrete road bridge. Specific techniques and extensions of the algorithm are used to overcome difficulties from the size of the structure which is associated with the number of recorded sensor channels as well as from the operational disturbances by a nearby construction site. It can be shown that for concrete bridges the proposed damage detection methodology is able to clearly indicate the presence of structural damage, if the damage leads to a significant change of the structural system. Small damage which do not result in a System change when not activated by loading, do not lead to a modification of the dynamic response behavior and for that cannot be detected with the proposed global monitoring method.

Fault detection and isolation can be handled by many different approaches. This paper builds upon a hypothesis test that checks whether the mean of a Gaussian random vector has become non-zero in the faulty state, based on a chi2 test. For fault isolation, it has to be decided which components in the parameter set of the Gaussian vector have changed, which is done by variants of the chi2 hypothesis test using the so-called sensitivity and minmax approaches. While only the sensitivity of the tested parameter component is taken into account in the sensitivity approach, the sensitivities of all parameters are used in the minmax approach, leading to better statistical properties at the expense of an increased computational burden. The computation of the respective test variable in the minmax test is cumbersome and may be ill-conditioned especially for large parameter sets, asking hence for a careful numerical evaluation. Furthermore, the fault isolation procedure requires the repetitive calculation of the test variable for each of the parameter components that are tested for a change, which may be a significant computational burden. In this paper, dealing with the minmax problem, we propose a new efficient computation for the test variables, which is based on a simultaneous QR decomposition for all parameters. Based on this scheme, we propose an efficient test computation for a large parameter set, leading to a decrease in the numerical complexity by one order of magnitude in the total number of parameters. Finally, we show how the minmax test is useful for structural damage localization, where an asymptotically Gaussian residual vector is computed from output-only vibration data of a mechanical or a civil structure.

Operational modal analysis and vibration based damage detection of engineering
structures have become important issues for Structural Health Monitoring (SHM) and
maintenance operations, e.g. on transport infrastructure. Methods from control
engineering have been adopted and converted for the application on civil structures.
Approaches like subspace-based system identification combine excellent theoretical
properties under the unknown excitation properties of a structure with practical
usefulness.
In this paper, the implementation of covariance-driven stochastic subspace
identification (SSI) on the smart wireless sensor platform PEGASE is described.
Special care is taken about the fast implementation of this technique since the
computations are embedded on the platform and perform in real-time. The most
efficient and current version of subspace algorithms has been implemented. Efficiency
and memory consumption are primary criteria in this implementation.
First validated results will be given for each step of the algorithms: crosscorrelation
on natural inputs signal from sensors; Hankel matrix output; SSI
implementation using the LAPACK library to get a SVD, pseudo-inverse, eigenvalues
etc. Results validation has been correlated between PEGASE implementation and the
previous processing in static situation: the same data was collected by wired sensors
and data-loggers, then, later, processed on a PC using traditional Matlab software.
In parallel, from an engineering point of view, a description of the PEGASE
wireless platform will be given: generic usage, wide capacities, embedded Digital
Signal Processing (DSP) processor and Library over a small embedded Linux
Operating System, a very accurate synchronization principle based on a GPS/PPS
principle, etc. Perspectives about a complete technical in-situ installation will also be
given.